Page 170 - Petrophysics
P. 170

PERMEABILITY-POROSITY  RELATIONSHIPS             143


                              Combining Equations 3.70 and 3.75 yields:



                                                                                           (3.77)


                              and the tortuosity is:






                                Using the same approach, the effects  of flow path on the permeability
                              can be evaluated. Applying Poiseiulle’s equation to the ith tube, the flow
                              rate in the ith tube, qi, is equal to:



                                                                                           (3.79)



                              where  rpai,  1, and  AP  are,  respectively,  the  apparent radius  of  the
                              ith tube, fluid viscosity, and pressure differential across the unit block.
                              For n tubes, the total flow rate q is:



                                                                                           (3.80)



                              and, assuming A2  is constant, the flow rate is:



                                                                                           (3.81)


                              Applying Darcy’s law to the unit block, the flow rate is equal to:



                                                                                           (3.82)


                              Combining Equations 3.76, 3.77, 3.79, 3.80, and 3.81, and solving for
                              the apparent permeability of the block, ka:



                                                                                           (3.83)
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